Precalculus Examples

$\log (\frac{12}{y})$

Step 1

Rewrite $\log (\frac{12}{y})$ as $\log (12) - \log (y)$ .

$\log (12) - \log (y)$

Step 2

Simplify each term.

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Step 2.1

Rewrite $\log (12)$ as $\log (2^{2} \cdot 3)$ .

$\log (2^{2} \cdot 3) - \log (y)$

Step 2.2

Rewrite $\log (2^{2} \cdot 3)$ as $\log (2^{2}) + \log (3)$ .

$\log (2^{2}) + \log (3) - \log (y)$

Step 2.3

Expand $\log (2^{2})$ by moving $2$ outside the logarithm.

$2 \log (2) + \log (3) - \log (y)$